Probability mass function problem

[mcafej]

Homework Statement

1. The sample space Ω of a certain experiment are the values 1, 2, 3, 4 and
5 and the probability assigned to a possible value w is proportional
to w².
(a) What is the probability mass function p(w) for this probability
space?
(b) What probability does this mass function assign to the interval
(1; 3]?

Homework Equations

The Attempt at a Solution

The hardest part for me to understand is the probabilities being proportional to w². I believe the probabilities for w are 1/15, 2/15, 3/15, 4/15 and 5/15, but I'm not sure. If somebody could clear this up for me it would really help. What does it mean for w to be proportional to w²?

 

[tiny-tim]

hi mcafej!

The hardest part for me to understand is the probabilities being proportional to w². I believe the probabilities for w are 1/15, 2/15, 3/15, 4/15 and 5/15, but I'm not sure. If somebody could clear this up for me it would really help. What does it mean for w to be proportional to w²?

call them A B C D and E instead of 1 2 3 4 and 5 …

then P(E) = 25P(A), P(D) = 16P(A), P(C) = 9P(A), P(B) = 4P(A) ​

 

[HallsofIvy]

Homework Statement

1. The sample space Ω of a certain experiment are the values 1, 2, 3, 4 and
5 and the probability assigned to a possible value w is proportional
to w².

That means that P(1)= k, P(2)= 2k, P(3)= 3k, P(4)= 4k, and P(5)= 5k for some number k.

(a) What is the probability mass function p(w) for this probability
space?

Use the fact that the probabilities must sum to 1 to find k.

(b) What probability does this mass function assign to the interval
(1; 3]?

That "interval" is really the set {2, 3} so the probability is P(2)+ P(3).

Homework Equations

The Attempt at a Solution

The hardest part for me to understand is the probabilities being proportional to w². I believe the probabilities for w are 1/15, 2/15, 3/15, 4/15 and 5/15, but I'm not sure. If somebody could clear this up for me it would really help. What does it mean for w to be proportional to w²?

 

[Ray Vickson]

Homework Statement

1. The sample space Ω of a certain experiment are the values 1, 2, 3, 4 and
5 and the probability assigned to a possible value w is proportional
to w².
(a) What is the probability mass function p(w) for this probability
space?
(b) What probability does this mass function assign to the interval
(1; 3]?

Homework Equations

The Attempt at a Solution

The hardest part for me to understand is the probabilities being proportional to w². I believe the probabilities for w are 1/15, 2/15, 3/15, 4/15 and 5/15, but I'm not sure. If somebody could clear this up for me it would really help. What does it mean for w to be proportional to w²?

It does NOT say that w is proportional to w^2; it says the probability of w is proportional to w^2. Just give the word "proportional" its usual meaning.